K alpha, K beta, L alpha, and L beta X-ray fluorescence cross sections for lanthanides in the atomic range 62 <= Z <= 68 (Sm, Eu, Gd Tb, Dy, Ho, and Er) were simultaneously measured by 59.54 keV incident photon energy at five angles ranging from 120 degrees to 160 degrees. The measurements were performed using an Am-241 radioisotope as the photon source and a Si(Li) detector. The L alpha X-ray fluorescence cross section (sigma(L alpha)) was found to decrease with increasing emission angle and showed an anisotropic distribution of L alpha X-rays. K alpha, K beta, and L beta X-ray fluorescence cross sections (sigma(K alpha), sigma(k beta), and sigma(L beta)) were observed to be angle-independent and showed an isotropic distribution of K alpha, K beta and L beta X-rays. The K alpha and K beta X-rays originate from filling of the K shell (J = 1/2) vacancies, L beta X-rays from filling of the L-1 and L-2 (J = 1/2) subshell vacancies, and L alpha X-rays from filling of the L-3 subshell (J = 3/2) vacancy. The fluorescent X-rays originating from the vacancy states with J = 1/2 are isotropic and unpolarized, but fluorescent X-rays originating from the vacancy states with J > 1/2 are anisotropic and polarized. Thus, the atomic inner shells vacancy states with J > 1/2 are aligned whereas vacancy states with J = 1/2 are not aligned. La fluorescence X-rays have an anisotropic distribution, while K alpha, K beta, and L beta fluorescence X-rays have isotropic distribution. Furthermore, the I-K beta/I-K alpha, I-L alpha/I-K alpha, I-L beta/I-K alpha, and I-L beta/I-L alpha intensity ratios for the elements under investigation were determined. The experimental cross sections and intensity ratios for K alpha, K beta, L alpha, and L beta fluorescence X-rays were also determined, and these experimental values were compared with our calculated theoretical values.